The notebook source code for this article is available on: GitCode, GitHub
MindSpore is an open source deep learning framework lead by Huawei and the MindSpore community. It is optimized for performing model training and inference tasks on Huawei’s Ascend series processors (NPUs), though it supports NVIDIA GPUs and CPU-only environments as well. It provides a compelling alternative to PyTorch, the leading open source deep learning framework under the Linux Foundation. Furthermore, it provides utility classes and functions compatible with a subset of PyTorch to ease the migration of training and inference pipelines from PyTorch to MindSpore, which is out of scope for this article.
In this lab, we will use MindSpore for training a simple linear regression model consisting of a single fully connected layer to predict house prices in California. The dataset we will be using is the California housing dataset which we’ll fetch using scikit-learn’s sklearn.datasets.fetch_california_housing function.
Prerequisites and suggested reading
The first 3 chapters of Dive into Deep Learning, also known as D2L. It covers the background knowledge on introductory probability, statistics and linear algebra, as well as data pre-processing, transformation methods and linear regression techniques required to understand the steps performed in this lab.
Software environment and dependencies
The instructions in this lab were tested on the OrangePi AIpro (20T) development board. It should work in a CPU-only environment as well with minimal configuration – simply specify the NOTEBOOK_USE_CPU=1 environment variable. While it may work in NVIDIA GPU environments with few modifications by specifying the NOTEBOOK_USE_GPU=1 environment variable, this has not been explicitly tested.
The software versions listed below which can be found in the provided requirements.txt as well.
- Python 3.12
- MindSpore 2.8.0
- CANN 8.5.0 – only on Ascend platform
- Matplotlib 3.10.8
- scikit-learn 1.8.0
%pip install -r requirements.txt
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--upgrade pip[0mNote: you may need to restart the kernel to use updated packages.
Initializing and checking MindSpore
Let’s initialize MindSpore based on our hardware platform and verify that it is correctly installed.
import osNOTEBOOK_USE_ASCEND = os.getenv('NOTEBOOK_USE_ASCEND', '0')NOTEBOOK_USE_GPU = os.getenv('NOTEBOOK_USE_GPU', '0')NOTEBOOK_USE_CPU = os.getenv('NOTEBOOK_USE_CPU', '0')NOTEBOOK_CI_MODE = os.getenv('NOTEBOOK_CI_MODE', '0')
import mindsporeplatform = 'Ascend'if NOTEBOOK_USE_ASCEND == '1': platform = 'Ascend'elif NOTEBOOK_USE_GPU == '1': platform = 'GPU'elif NOTEBOOK_USE_CPU == '1' or NOTEBOOK_CI_MODE == '1': platform = 'CPU'else: platform = 'Ascend'mindspore.set_device(device_target=platform)mindspore.run_check()
/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/unify_schedule/vector/transdata/common/graph/transdata_graph_info.py:146: SyntaxWarning: invalid escape sequence '\c' 2. In forward, tiling would not split c1 and c0, find c1\c0 based on t2./usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/unify_schedule/vector/transdata/common/graph/transdata_graph_info.py:172: SyntaxWarning: invalid escape sequence '\c' 1. Forward: tiling would not split c1\c0\h0, find c1\c0\h1\h0 based on t2/home/HwHiAiUser/.pyenv/versions/3.12.13/envs/orangepiaipro-20t/lib/python3.12/site-packages/numpy/core/getlimits.py:549: UserWarning: The value of the smallest subnormal for <class 'numpy.float32'> type is zero. setattr(self, word, getattr(machar, word).flat[0])/home/HwHiAiUser/.pyenv/versions/3.12.13/envs/orangepiaipro-20t/lib/python3.12/site-packages/numpy/core/getlimits.py:89: UserWarning: The value of the smallest subnormal for <class 'numpy.float32'> type is zero. return self._float_to_str(self.smallest_subnormal)/home/HwHiAiUser/.pyenv/versions/3.12.13/envs/orangepiaipro-20t/lib/python3.12/site-packages/numpy/core/getlimits.py:549: UserWarning: The value of the smallest subnormal for <class 'numpy.float64'> type is zero. setattr(self, word, getattr(machar, word).flat[0])/home/HwHiAiUser/.pyenv/versions/3.12.13/envs/orangepiaipro-20t/lib/python3.12/site-packages/numpy/core/getlimits.py:89: UserWarning: The value of the smallest subnormal for <class 'numpy.float64'> type is zero. return self._float_to_str(self.smallest_subnormal)MindSpore version: 2.8.0The result of multiplication calculation is correct, MindSpore has been installed on platform [Ascend] successfully!
Warnings can be safely ignored as long as no [CRITICAL] or [ERROR] messages appear, in which case check out the Ascend forum. If you see the below output, it means MindSpore 2.8.0 is correctly installed.
MindSpore version: 2.8.0The result of multiplication calculation is correct, MindSpore has been installed on platform [Ascend] successfully!
Loading and transforming the data
Let’s fetch the California housing dataset with scikit-learn’s fetch_california_housing. We’ll convert the target to have shape (20640, 1), to avoid issues with our linear regression algorithm due to broadcasting.
from sklearn.datasets import fetch_california_housinghousing = fetch_california_housing()X = housing.datay = housing.target.reshape(-1, 1)X.shape, y.shape
((20640, 8), (20640, 1))
Split the dataset into training and validation sets. We’ll use an $80:20$ ratio which is common in many machine learning applications.
from sklearn.model_selection import train_test_splitX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, shuffle=False)X_train.shape, X_test.shape, y_train.shape, y_test.shape
((16512, 8), (4128, 8), (16512, 1), (4128, 1))
Let’s inspect the first sample in our training set. Notice that all features and labels are purely numeric, floating point values – a perfect example of using linear regression.
X_train[0], y_train[0]
(array([ 8.3252 , 41. , 6.98412698, 1.02380952, 322. , 2.55555556, 37.88 , -122.23 ]), array([4.526]))
Verify that our data is clean with no NaN values.
import numpy as npnp.any(np.isnan(X).ravel()), np.any(np.isnan(y).ravel())
(False, False)
Great – none of our samples contain NaNs! Let’s compute the mean and standard deviation of the labels in our training set.
y_train.mean(), y_train.std()
(2.02067031310562, 1.1352013072688294)
The scikit-learn documentation on real-world datasets states that the house prices are given as multiples of USD\$100,000 so the label values range from $0.15$ through $5.0$. Nevertheless, it’s a good idea to transform the labels through the 2-step process described below to make the data more Gaussian and centered, which should help our linear regression model produce more accurate results.
- Compute $\log(1 + y_i)$ for each label $y_i$. The additional unit translation within the logarithm avoids issues with zero values since $\log 0$ is undefined, even though we don’t expect any of our housing prices to be $0$
- Apply the
StandardScalerto the results in (1) to normalize the distribution to have zero mean $\mu = 0$ and unit variance $\sigma^2 = 1$
We’ll achieve this through a custom scaler class HousingPriceScaler which inherits the following base classes in scikit-learn.
sklearn.base.BaseEstimator: base class for all estimators in scikit-learnsklearn.base.TransformerMixin: base class for data transformation in scikit-learn
from sklearn.base import BaseEstimator, TransformerMixinfrom sklearn.preprocessing import StandardScalerclass HousingPriceScaler(BaseEstimator, TransformerMixin): def __init__(self): self.scaler = StandardScaler() def fit(self, y): y_log1p = np.log1p(y) print(f'After log1p, before scaling: mean = {y_log1p.mean():.4f}, stddev = {y_log1p.std():.4f}') self.scaler.fit(y_log1p) return self def transform(self, y): y_log1p = np.log1p(y) y_scaled = self.scaler.transform(y_log1p) return y_scaled def inverse_transform(self, y_scaled): y_log1p = self.scaler.inverse_transform(y_scaled) y = np.expm1(y_log1p) return yscaler = HousingPriceScaler()scaler
HousingPriceScaler
iParameters
Before scaling the labels, let’s scale the features as well. Unlike the labels which should be transformed via the 2-step process described above for optimal linear regression behavior, it suffices to normalize our features directly with sklearn.preprocessing.StandardScaler. This makes our scaled features have mean $\mu = 0$ and standard deviation $\sigma = 1$.
features_scaler = StandardScaler()X_train_scaled = features_scaler.fit_transform(X_train)print(f'Before scaling: mean = {X_train.mean():.4f}, stddev = {X_train.std():.4f}')print(f'After scaling: mean = {X_train_scaled.mean():.4f}, stddev = {X_train_scaled.std():.4f}')X_test_scaled = features_scaler.transform(X_test)
Before scaling: mean = 174.5399, stddev = 631.1331After scaling: mean = -0.0000, stddev = 1.0000
Now transform the labels in our training set with our custom scaler and observe the transformed labels are also centered with mean $\mu = 0$ and standard deviation $\sigma = 1$.
y_train_scaled = scaler.fit_transform(y_train)print(f'Before scaling: mean = {y_train.mean():.4f}, stddev = {y_train.std():.4f}')print(f'After scaling: mean = {y_train_scaled.mean():.4f}, stddev = {y_train_scaled.std():.4f}')y_test_scaled = scaler.transform(y_test)
After log1p, before scaling: mean = 1.0418, stddev = 0.3506Before scaling: mean = 2.0207, stddev = 1.1352After scaling: mean = 0.0000, stddev = 1.0000
With our training labels appropriately scaled, it’s time to define and train our neural network!
Defining and training our linear regression model
Let’s define a simple neural network with exactly 1 fully connected layer. The fully connected layer has 8 input channels and 1 output channel which corresponds to the number of features and labels in our dataset respectively.
With MindSpore, we do this by defining our own class inheriting from mindspore.nn.Cell and implement the construct method. Our fully connected layer is given by mindspore.nn.Dense.
Let’s also define our class to accept the following optional parameters.
lr: the learning rate of our model. Defaults to0.01if not specifiedwd: the weight decay factor $\lambda$. Defaults to0.0if not specified
Note that we must use 16-bit floating point values defined as float16 in mindspore.dtype. This is because matrix-vector and matrix-matrix multiplication is defined only for 16-bit floats with the CANN kernels library for the Ascend 310B1 NPU chip included with the OrangePi AIpro (20T) development board. This will reduce the precision of our model which is necessary and sufficient for our use case.
import mindspore.nn as nnfrom mindspore import dtype as mstypeclass MyModel(nn.Cell): def __init__(self, lr=0.01, wd=0.0): super().__init__() self.lr = lr self.wd = wd self.dense1 = nn.Dense(8, 1, dtype=mstype.float16) def construct(self, X): y_hat = self.dense1(X) return y_hatmodel = MyModel(lr=0.03, wd=0.0)model
MyModel( (dense1): Dense(input_channels=8, output_channels=1, has_bias=True))
Use the mean squared error (MSE) for our loss function, predefined in MindSpore with mindspore.nn.MSELoss.
loss_fn = nn.MSELoss()loss_fn
MSELoss()
Use minibatch stochaistic gradient descent (SGD) for our optimizer, predefined in MindSpore with mindspore.nn.SGD. Pass in the learning rate and weight decay factor from our model via the learning_rate and weight_decay arguments, respectively.
optimizer = nn.SGD(params=model.trainable_params(), learning_rate=model.lr, weight_decay=model.wd)optimizer
SGD()
Now define our forward and gradient functions. mindspore.value_and_grad accepts the following parameters.
fn: our forward function. It takes the featuresXand labelsyas arguments and returns a tuple of(loss, prediction)grad_position: set it toNoneand differentiate based on the model weights insteadweights: pass in the model weights available through our optimizer asoptimizer.parametershas_aux: set toTrueso it returns the gradient based on just the first argumentloss
def forward_fn(X, y): y_hat = model(X) loss = loss_fn(y_hat, y) return loss, y_hatgrad_fn = mindspore.value_and_grad(fn=forward_fn, grad_position=None, weights=optimizer.parameters, has_aux=True)
Define our training step and training epoch. Each step we take a batch of a certain fixed size, usually a power of 2, e.g. $2^9=512$. 1 full pass on our training data is known as an epoch.
def train_step(X, y): (loss, _), grads = grad_fn(X, y) optimizer(grads) return lossdef train_epoch(dataset, epoch=0): model.set_train() print(f'Epoch {epoch} start') batch_total = dataset.get_dataset_size() training_losses = [] for batch_idx, (X_batch, y_batch) in enumerate(dataset.create_tuple_iterator()): loss = train_step(X_batch, y_batch) print(f'Training loss (scaled): {loss.asnumpy():.4f} [{batch_idx}/{batch_total}]') training_losses.append(loss) print(f'Epoch {epoch} end') return training_losses
At the end of each epoch, let’s also validate our model against the validation set. Recall that our model was trained on features normalized by StandardScaler, plus labels that have undergone the 2-step transformation described in an earlier section. It will return predictions which are similarly transformed. We can undo these transformations with the inverse_transform method of our scaler class, which gives us the predicted house prices in multiples of USD\$100,000.
def validate_epoch(epoch=0): model.set_train(False) y_hat_scaled = model(mindspore.Tensor(X_test_scaled.astype(np.float16))).asnumpy() y_hat = scaler.inverse_transform(y_hat_scaled) validation_loss_scaled = loss_fn(mindspore.Tensor(y_hat_scaled), mindspore.Tensor(y_test_scaled)) validation_loss = loss_fn(mindspore.Tensor(y_hat), mindspore.Tensor(y_test)) print(f'Validation loss at epoch {epoch} (scaled): {validation_loss_scaled.asnumpy():.4f}') print(f'Validation loss at epoch {epoch}: {validation_loss.asnumpy():.4f}') return validation_loss_scaled
Convert our dataset to mindspore.dataset.NumpySlicesDataset and feed it to our model in batches of $2^9=512$ samples per batch. We saw some of its included methods in the train_epoch function.
get_dataset_size: get the total number of batches in the datasetcreate_tuple_iterator: convert the dataset into an iterator of tuples in the form(batch_idx, (X_batch, y_batch))
import mindspore.dataset as dsimport mindspore.ops as opstrain_ds = ds.NumpySlicesDataset(data=(X_train_scaled.astype(np.float16), y_train_scaled.astype(np.float16)), column_names=['features', 'labels'])train_ds = train_ds.batch(batch_size=512)epochs = 15training_losses_scaled = []validation_losses_scaled = []for epoch_idx in range(epochs): training_losses_scaled.extend(train_epoch(train_ds, epoch=epoch_idx)) validation_losses_scaled.append(validate_epoch(epoch=epoch_idx))training_losses_scaled = ops.cast(ops.stack(training_losses_scaled, axis=0), dtype=mstype.float64)validation_losses_scaled = ops.stack(validation_losses_scaled, axis=0)training_losses_scaled.shape, validation_losses_scaled.shape
Epoch 0 start/usr/local/Ascend/cann-8.5.0/python/site-packages/asc_op_compile_base/asc_op_compiler/ascendc_compile_gen_code.py:161: SyntaxWarning: invalid escape sequence '\w' match = re.search(f'{option}=(\w+)', ' '.join(compile_options))/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/classifier/transdata/transdata_classifier.py:223: SyntaxWarning: invalid escape sequence '\B' Return BN\BH SCH Result/usr/local/Ascend/cann-8.5.0/python/site-packages/tbe/dsl/unify_schedule/vector/transdata/common/graph/transdata_graph_info.py:146: SyntaxWarning: invalid escape sequence '\c' 2. 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Forward: tiling would not split c1\c0\h0, find c1\c0\h1\h0 based on t2/usr/local/Ascend/cann-8.5.0/opp/built-in/op_impl/ai_core/tbe/impl/ops_legacy/dynamic/gelu_grad_v2.py:97: SyntaxWarning: invalid escape sequence '\h' gelu_grad_erf = erfc(-\hat{x}) / 2 + (1 /sqrt(Pi)) * (\hat{x}) * exp(-\hat{x}^2)/usr/local/Ascend/cann-8.5.0/opp/built-in/op_impl/ai_core/tbe/impl/ops_legacy/dynamic/gelu_grad_v2.py:157: SyntaxWarning: invalid escape sequence '\h' gelu_grad_erf = erfc(-\hat{x}) / 2 + (1 /sqrt(Pi)) * (\hat{x}) * exp(-\hat{x}^2)/usr/local/Ascend/cann-8.5.0/python/site-packages/asc_op_compile_base/asc_op_compiler/ascendc_compile_gen_code.py:161: SyntaxWarning: invalid escape sequence '\w' match = re.search(f'{option}=(\w+)', ' '.join(compile_options))/usr/local/Ascend/cann-8.5.0/python/site-packages/asc_op_compile_base/asc_op_compiler/ascendc_compile_gen_code.py:161: SyntaxWarning: invalid escape sequence '\w' match = re.search(f'{option}=(\w+)', ' '.join(compile_options))/usr/local/Ascend/cann-8.5.0/python/site-packages/asc_op_compile_base/asc_op_compiler/ascendc_compile_gen_code.py:161: SyntaxWarning: invalid escape sequence '\w' match = re.search(f'{option}=(\w+)', ' '.join(compile_options))/usr/local/Ascend/cann-8.5.0/python/site-packages/asc_op_compile_base/asc_op_compiler/ascendc_compile_gen_code.py:161: SyntaxWarning: invalid escape sequence '\w' match = re.search(f'{option}=(\w+)', ' '.join(compile_options))/usr/local/Ascend/cann-8.5.0/python/site-packages/asc_op_compile_base/asc_op_compiler/ascendc_compile_gen_code.py:161: SyntaxWarning: invalid escape sequence '\w' match = re.search(f'{option}=(\w+)', ' '.join(compile_options))/usr/local/Ascend/cann-8.5.0/python/site-packages/asc_op_compile_base/asc_op_compiler/ascendc_compile_gen_code.py:161: SyntaxWarning: invalid escape sequence '\w' match = re.search(f'{option}=(\w+)', ' '.join(compile_options))/usr/local/Ascend/cann-8.5.0/python/site-packages/asc_op_compile_base/asc_op_compiler/ascendc_compile_gen_code.py:161: SyntaxWarning: invalid escape sequence '\w' match = re.search(f'{option}=(\w+)', ' '.join(compile_options))/usr/local/Ascend/cann-8.5.0/python/site-packages/asc_op_compile_base/asc_op_compiler/ascendc_compile_gen_code.py:161: SyntaxWarning: invalid escape sequence '\w' match = re.search(f'{option}=(\w+)', ' '.join(compile_options)).Training loss (scaled): 1.3799 [0/33]Training loss (scaled): 1.2891 [1/33]Training loss (scaled): 1.1133 [2/33]Training loss (scaled): 1.0420 [3/33]Training loss (scaled): 0.9453 [4/33]Training loss (scaled): 1.2617 [5/33]Training loss (scaled): 0.8091 [6/33]Training loss (scaled): 0.7905 [7/33]Training loss (scaled): 0.7300 [8/33]Training loss (scaled): 0.6133 [9/33]Training loss (scaled): 0.6831 [10/33]Training loss (scaled): 0.6797 [11/33]Training loss (scaled): 0.7168 [12/33]Training loss (scaled): 0.6226 [13/33]Training loss (scaled): 0.7051 [14/33]Training loss (scaled): 0.5557 [15/33]Training loss (scaled): 0.5259 [16/33]Training loss (scaled): 0.5215 [17/33]Training loss (scaled): 0.4946 [18/33]Training loss (scaled): 0.4644 [19/33]Training loss (scaled): 0.4788 [20/33]Training loss (scaled): 0.4482 [21/33]Training loss (scaled): 0.4346 [22/33]Training loss (scaled): 0.4951 [23/33]Training loss (scaled): 0.5820 [24/33]Training loss (scaled): 0.4407 [25/33]Training loss (scaled): 0.6157 [26/33]Training loss (scaled): 0.4985 [27/33]Training loss (scaled): 1.1260 [28/33]Training loss (scaled): 0.5576 [29/33]Training loss (scaled): 0.5366 [30/33]Training loss (scaled): 0.5557 [31/33]Training loss (scaled): 0.4836 [32/33]Epoch 0 endValidation loss at epoch 0 (scaled): 0.5919Validation loss at epoch 0: 284.3527Epoch 1 startTraining loss (scaled): 0.4980 [0/33]Training loss (scaled): 0.5049 [1/33]Training loss (scaled): 0.4485 [2/33]Training loss (scaled): 0.4717 [3/33]Training loss (scaled): 0.4900 [4/33]Training loss (scaled): 0.4839 [5/33]Training loss (scaled): 0.5483 [6/33]Training loss (scaled): 0.4541 [7/33]Training loss (scaled): 0.5259 [8/33]Training loss (scaled): 0.4878 [9/33]Training loss (scaled): 0.4846 [10/33]Training loss (scaled): 0.5684 [11/33]Training loss (scaled): 0.4893 [12/33]Training loss (scaled): 0.4773 [13/33]Training loss (scaled): 0.4653 [14/33]Training loss (scaled): 0.4905 [15/33]Training loss (scaled): 0.4165 [16/33]Training loss (scaled): 0.4250 [17/33]Training loss (scaled): 0.4495 [18/33]Training loss (scaled): 0.4648 [19/33]Training loss (scaled): 0.5757 [20/33]Training loss (scaled): 0.4775 [21/33]Training loss (scaled): 0.4695 [22/33]Training loss (scaled): 0.5386 [23/33]Training loss (scaled): 0.4153 [24/33]Training loss (scaled): 0.5107 [25/33]Training loss (scaled): 0.5142 [26/33]Training loss (scaled): 0.4727 [27/33]Training loss (scaled): 0.4907 [28/33]Training loss (scaled): 0.4236 [29/33]Training loss (scaled): 0.4270 [30/33]Training loss (scaled): 0.4553 [31/33]Training loss (scaled): 0.3872 [32/33]Epoch 1 endValidation loss at epoch 1 (scaled): 0.4860Validation loss at epoch 1: 0.7928Epoch 2 startTraining loss (scaled): 0.4849 [0/33]Training loss (scaled): 0.4739 [1/33]Training loss (scaled): 0.4854 [2/33]Training loss (scaled): 0.4985 [3/33]Training loss (scaled): 0.4985 [4/33]Training loss (scaled): 0.4639 [5/33]Training loss (scaled): 0.4258 [6/33]Training loss (scaled): 0.5562 [7/33]Training loss (scaled): 0.4263 [8/33]Training loss (scaled): 0.3901 [9/33]Training loss (scaled): 0.4709 [10/33]Training loss (scaled): 0.4087 [11/33]Training loss (scaled): 0.5078 [12/33]Training loss (scaled): 0.4644 [13/33]Training loss (scaled): 0.4473 [14/33]Training loss (scaled): 0.4390 [15/33]Training loss (scaled): 0.4197 [16/33]Training loss (scaled): 0.4197 [17/33]Training loss (scaled): 0.5298 [18/33]Training loss (scaled): 0.4229 [19/33]Training loss (scaled): 0.4641 [20/33]Training loss (scaled): 0.4233 [21/33]Training loss (scaled): 0.4404 [22/33]Training loss (scaled): 0.5151 [23/33]Training loss (scaled): 0.5049 [24/33]Training loss (scaled): 0.4377 [25/33]Training loss (scaled): 0.5542 [26/33]Training loss (scaled): 0.4241 [27/33]Training loss (scaled): 0.4631 [28/33]Training loss (scaled): 0.4189 [29/33]Training loss (scaled): 0.3826 [30/33]Training loss (scaled): 0.4807 [31/33]Training loss (scaled): 0.4712 [32/33]Epoch 2 endValidation loss at epoch 2 (scaled): 0.4533Validation loss at epoch 2: 0.8286Epoch 3 startTraining loss (scaled): 0.5015 [0/33]Training loss (scaled): 0.5015 [1/33]Training loss (scaled): 0.4878 [2/33]Training loss (scaled): 0.4609 [3/33]Training loss (scaled): 0.4365 [4/33]Training loss (scaled): 0.4392 [5/33]Training loss (scaled): 0.4238 [6/33]Training loss (scaled): 0.4951 [7/33]Training loss (scaled): 0.4319 [8/33]Training loss (scaled): 0.4109 [9/33]Training loss (scaled): 0.5068 [10/33]Training loss (scaled): 0.4204 [11/33]Training loss (scaled): 0.4448 [12/33]Training loss (scaled): 0.4456 [13/33]Training loss (scaled): 0.4688 [14/33]Training loss (scaled): 0.4763 [15/33]Training loss (scaled): 0.4114 [16/33]Training loss (scaled): 0.4299 [17/33]Training loss (scaled): 0.4363 [18/33]Training loss (scaled): 0.3933 [19/33]Training loss (scaled): 0.4175 [20/33]Training loss (scaled): 0.4856 [21/33]Training loss (scaled): 0.5078 [22/33]Training loss (scaled): 0.4187 [23/33]Training loss (scaled): 0.4204 [24/33]Training loss (scaled): 0.5415 [25/33]Training loss (scaled): 0.3647 [26/33]Training loss (scaled): 0.4138 [27/33]Training loss (scaled): 0.4194 [28/33]Training loss (scaled): 0.4302 [29/33]Training loss (scaled): 0.4780 [30/33]Training loss (scaled): 0.3928 [31/33]Training loss (scaled): 0.4355 [32/33]Epoch 3 endValidation loss at epoch 3 (scaled): 0.4293Validation loss at epoch 3: 0.7472Epoch 4 startTraining loss (scaled): 0.4875 [0/33]Training loss (scaled): 0.4434 [1/33]Training loss (scaled): 0.3662 [2/33]Training loss (scaled): 0.4177 [3/33]Training loss (scaled): 0.4675 [4/33]Training loss (scaled): 0.4407 [5/33]Training loss (scaled): 0.4023 [6/33]Training loss (scaled): 0.4033 [7/33]Training loss (scaled): 0.5107 [8/33]Training loss (scaled): 0.4307 [9/33]Training loss (scaled): 0.4255 [10/33]Training loss (scaled): 0.4106 [11/33]Training loss (scaled): 0.4382 [12/33]Training loss (scaled): 0.4121 [13/33]Training loss (scaled): 0.4995 [14/33]Training loss (scaled): 0.4846 [15/33]Training loss (scaled): 0.4290 [16/33]Training loss (scaled): 0.4783 [17/33]Training loss (scaled): 0.4761 [18/33]Training loss (scaled): 0.4272 [19/33]Training loss (scaled): 0.4092 [20/33]Training loss (scaled): 0.4395 [21/33]Training loss (scaled): 0.3760 [22/33]Training loss (scaled): 0.4736 [23/33]Training loss (scaled): 0.4136 [24/33]Training loss (scaled): 0.4019 [25/33]Training loss (scaled): 0.5293 [26/33]Training loss (scaled): 0.4460 [27/33]Training loss (scaled): 0.4272 [28/33]Training loss (scaled): 0.4282 [29/33]Training loss (scaled): 0.4248 [30/33]Training loss (scaled): 0.4141 [31/33]Training loss (scaled): 0.4194 [32/33]Epoch 4 endValidation loss at epoch 4 (scaled): 0.4155Validation loss at epoch 4: 0.7660Epoch 5 startTraining loss (scaled): 0.4307 [0/33]Training loss (scaled): 0.4094 [1/33]Training loss (scaled): 0.4468 [2/33]Training loss (scaled): 0.4265 [3/33]Training loss (scaled): 0.4500 [4/33]Training loss (scaled): 0.4451 [5/33]Training loss (scaled): 0.4629 [6/33]Training loss (scaled): 0.4011 [7/33]Training loss (scaled): 0.3989 [8/33]Training loss (scaled): 0.4148 [9/33]Training loss (scaled): 0.4294 [10/33]Training loss (scaled): 0.3813 [11/33]Training loss (scaled): 0.4500 [12/33]Training loss (scaled): 0.4382 [13/33]Training loss (scaled): 0.4919 [14/33]Training loss (scaled): 0.4407 [15/33]Training loss (scaled): 0.4353 [16/33]Training loss (scaled): 0.3940 [17/33]Training loss (scaled): 0.4619 [18/33]Training loss (scaled): 0.3779 [19/33]Training loss (scaled): 0.4795 [20/33]Training loss (scaled): 0.4648 [21/33]Training loss (scaled): 0.3726 [22/33]Training loss (scaled): 0.4307 [23/33]Training loss (scaled): 0.4753 [24/33]Training loss (scaled): 0.4597 [25/33]Training loss (scaled): 0.3872 [26/33]Training loss (scaled): 0.4868 [27/33]Training loss (scaled): 0.3879 [28/33]Training loss (scaled): 0.3955 [29/33]Training loss (scaled): 0.4275 [30/33]Training loss (scaled): 0.4331 [31/33]Training loss (scaled): 0.3843 [32/33]Epoch 5 endValidation loss at epoch 5 (scaled): 0.3980Validation loss at epoch 5: 0.7297Epoch 6 startTraining loss (scaled): 0.3804 [0/33]Training loss (scaled): 0.4395 [1/33]Training loss (scaled): 0.3594 [2/33]Training loss (scaled): 0.4094 [3/33]Training loss (scaled): 0.4695 [4/33]Training loss (scaled): 0.4031 [5/33]Training loss (scaled): 0.4036 [6/33]Training loss (scaled): 0.4141 [7/33]Training loss (scaled): 0.4409 [8/33]Training loss (scaled): 0.4438 [9/33]Training loss (scaled): 0.4038 [10/33]Training loss (scaled): 0.4348 [11/33]Training loss (scaled): 0.4473 [12/33]Training loss (scaled): 0.4678 [13/33]Training loss (scaled): 0.4485 [14/33]Training loss (scaled): 0.4634 [15/33]Training loss (scaled): 0.4153 [16/33]Training loss (scaled): 0.3677 [17/33]Training loss (scaled): 0.4082 [18/33]Training loss (scaled): 0.4609 [19/33]Training loss (scaled): 0.4353 [20/33]Training loss (scaled): 0.4473 [21/33]Training loss (scaled): 0.3916 [22/33]Training loss (scaled): 0.3882 [23/33]Training loss (scaled): 0.4001 [24/33]Training loss (scaled): 0.4312 [25/33]Training loss (scaled): 0.4265 [26/33]Training loss (scaled): 0.4602 [27/33]Training loss (scaled): 0.4067 [28/33]Training loss (scaled): 0.5522 [29/33]Training loss (scaled): 0.3811 [30/33]Training loss (scaled): 0.4260 [31/33]Training loss (scaled): 0.3186 [32/33]Epoch 6 endValidation loss at epoch 6 (scaled): 0.3879Validation loss at epoch 6: 0.7155Epoch 7 startTraining loss (scaled): 0.3860 [0/33]Training loss (scaled): 0.3933 [1/33]Training loss (scaled): 0.3569 [2/33]Training loss (scaled): 0.4600 [3/33]Training loss (scaled): 0.4119 [4/33]Training loss (scaled): 0.5010 [5/33]Training loss (scaled): 0.3506 [6/33]Training loss (scaled): 0.3987 [7/33]Training loss (scaled): 0.4194 [8/33]Training loss (scaled): 0.4277 [9/33]Training loss (scaled): 0.4182 [10/33]Training loss (scaled): 0.3855 [11/33]Training loss (scaled): 0.4700 [12/33]Training loss (scaled): 0.3882 [13/33]Training loss (scaled): 0.4424 [14/33]Training loss (scaled): 0.4597 [15/33]Training loss (scaled): 0.3625 [16/33]Training loss (scaled): 0.4492 [17/33]Training loss (scaled): 0.3894 [18/33]Training loss (scaled): 0.4302 [19/33]Training loss (scaled): 0.6040 [20/33]Training loss (scaled): 0.4192 [21/33]Training loss (scaled): 0.4119 [22/33]Training loss (scaled): 0.3787 [23/33]Training loss (scaled): 0.4592 [24/33]Training loss (scaled): 0.3889 [25/33]Training loss (scaled): 0.4431 [26/33]Training loss (scaled): 0.4304 [27/33]Training loss (scaled): 0.4224 [28/33]Training loss (scaled): 0.4387 [29/33]Training loss (scaled): 0.3936 [30/33]Training loss (scaled): 0.4045 [31/33]Training loss (scaled): 0.4368 [32/33]Epoch 7 endValidation loss at epoch 7 (scaled): 0.3768Validation loss at epoch 7: 0.7110Epoch 8 startTraining loss (scaled): 0.4438 [0/33]Training loss (scaled): 0.3782 [1/33]Training loss (scaled): 0.4084 [2/33]Training loss (scaled): 0.3774 [3/33]Training loss (scaled): 0.4077 [4/33]Training loss (scaled): 0.4534 [5/33]Training loss (scaled): 0.3889 [6/33]Training loss (scaled): 0.4089 [7/33]Training loss (scaled): 0.3799 [8/33]Training loss (scaled): 0.4436 [9/33]Training loss (scaled): 0.4214 [10/33]Training loss (scaled): 0.4421 [11/33]Training loss (scaled): 0.4214 [12/33]Training loss (scaled): 0.3994 [13/33]Training loss (scaled): 0.4077 [14/33]Training loss (scaled): 0.4004 [15/33]Training loss (scaled): 0.4548 [16/33]Training loss (scaled): 0.4453 [17/33]Training loss (scaled): 0.4199 [18/33]Training loss (scaled): 0.4426 [19/33]Training loss (scaled): 0.3887 [20/33]Training loss (scaled): 0.4299 [21/33]Training loss (scaled): 0.4333 [22/33]Training loss (scaled): 0.4502 [23/33]Training loss (scaled): 0.4641 [24/33]Training loss (scaled): 0.3931 [25/33]Training loss (scaled): 0.4053 [26/33]Training loss (scaled): 0.4231 [27/33]Training loss (scaled): 0.4282 [28/33]Training loss (scaled): 0.4646 [29/33]Training loss (scaled): 0.3545 [30/33]Training loss (scaled): 0.3992 [31/33]Training loss (scaled): 0.4082 [32/33]Epoch 8 endValidation loss at epoch 8 (scaled): 0.3708Validation loss at epoch 8: 0.6989Epoch 9 startTraining loss (scaled): 0.3257 [0/33]Training loss (scaled): 0.3926 [1/33]Training loss (scaled): 0.4119 [2/33]Training loss (scaled): 0.5244 [3/33]Training loss (scaled): 0.4785 [4/33]Training loss (scaled): 0.4290 [5/33]Training loss (scaled): 0.4595 [6/33]Training loss (scaled): 0.4036 [7/33]Training loss (scaled): 0.4187 [8/33]Training loss (scaled): 0.4075 [9/33]Training loss (scaled): 0.3384 [10/33]Training loss (scaled): 0.4338 [11/33]Training loss (scaled): 0.4077 [12/33]Training loss (scaled): 0.4485 [13/33]Training loss (scaled): 0.4392 [14/33]Training loss (scaled): 0.3640 [15/33]Training loss (scaled): 0.3997 [16/33]Training loss (scaled): 0.4136 [17/33]Training loss (scaled): 0.3755 [18/33]Training loss (scaled): 0.4504 [19/33]Training loss (scaled): 0.4307 [20/33]Training loss (scaled): 0.4619 [21/33]Training loss (scaled): 0.3486 [22/33]Training loss (scaled): 0.4304 [23/33]Training loss (scaled): 0.3750 [24/33]Training loss (scaled): 0.4080 [25/33]Training loss (scaled): 0.4058 [26/33]Training loss (scaled): 0.4558 [27/33]Training loss (scaled): 0.4185 [28/33]Training loss (scaled): 0.4119 [29/33]Training loss (scaled): 0.4121 [30/33]Training loss (scaled): 0.3945 [31/33]Training loss (scaled): 0.4443 [32/33]Epoch 9 endValidation loss at epoch 9 (scaled): 0.3671Validation loss at epoch 9: 0.7032Epoch 10 startTraining loss (scaled): 0.4160 [0/33]Training loss (scaled): 0.3657 [1/33]Training loss (scaled): 0.4250 [2/33]Training loss (scaled): 0.3606 [3/33]Training loss (scaled): 0.4211 [4/33]Training loss (scaled): 0.4133 [5/33]Training loss (scaled): 0.4048 [6/33]Training loss (scaled): 0.5000 [7/33]Training loss (scaled): 0.3999 [8/33]Training loss (scaled): 0.4199 [9/33]Training loss (scaled): 0.4463 [10/33]Training loss (scaled): 0.3999 [11/33]Training loss (scaled): 0.3787 [12/33]Training loss (scaled): 0.3945 [13/33]Training loss (scaled): 0.4580 [14/33]Training loss (scaled): 0.4402 [15/33]Training loss (scaled): 0.4546 [16/33]Training loss (scaled): 0.3735 [17/33]Training loss (scaled): 0.4141 [18/33]Training loss (scaled): 0.4097 [19/33]Training loss (scaled): 0.3789 [20/33]Training loss (scaled): 0.3848 [21/33]Training loss (scaled): 0.3628 [22/33]Training loss (scaled): 0.3931 [23/33]Training loss (scaled): 0.4067 [24/33]Training loss (scaled): 0.4187 [25/33]Training loss (scaled): 0.4050 [26/33]Training loss (scaled): 0.3977 [27/33]Training loss (scaled): 0.3567 [28/33]Training loss (scaled): 0.4460 [29/33]Training loss (scaled): 0.4719 [30/33]Training loss (scaled): 0.4302 [31/33]Training loss (scaled): 0.4878 [32/33]Epoch 10 endValidation loss at epoch 10 (scaled): 0.3616Validation loss at epoch 10: 0.7103Epoch 11 startTraining loss (scaled): 0.4387 [0/33]Training loss (scaled): 0.4246 [1/33]Training loss (scaled): 0.4741 [2/33]Training loss (scaled): 0.4214 [3/33]Training loss (scaled): 0.3855 [4/33]Training loss (scaled): 0.4331 [5/33]Training loss (scaled): 0.3752 [6/33]Training loss (scaled): 0.3652 [7/33]Training loss (scaled): 0.4309 [8/33]Training loss (scaled): 0.3799 [9/33]Training loss (scaled): 0.4414 [10/33]Training loss (scaled): 0.4143 [11/33]Training loss (scaled): 0.3821 [12/33]Training loss (scaled): 0.3503 [13/33]Training loss (scaled): 0.4426 [14/33]Training loss (scaled): 0.3931 [15/33]Training loss (scaled): 0.4011 [16/33]Training loss (scaled): 0.4319 [17/33]Training loss (scaled): 0.4209 [18/33]Training loss (scaled): 0.4080 [19/33]Training loss (scaled): 0.5190 [20/33]Training loss (scaled): 0.4082 [21/33]Training loss (scaled): 0.4209 [22/33]Training loss (scaled): 0.3794 [23/33]Training loss (scaled): 0.3772 [24/33]Training loss (scaled): 0.3721 [25/33]Training loss (scaled): 0.4241 [26/33]Training loss (scaled): 0.4021 [27/33]Training loss (scaled): 0.3865 [28/33]Training loss (scaled): 0.4167 [29/33]Training loss (scaled): 0.4834 [30/33]Training loss (scaled): 0.3765 [31/33]Training loss (scaled): 0.3296 [32/33]Epoch 11 endValidation loss at epoch 11 (scaled): 0.3568Validation loss at epoch 11: 0.7126Epoch 12 startTraining loss (scaled): 0.3965 [0/33]Training loss (scaled): 0.3430 [1/33]Training loss (scaled): 0.4348 [2/33]Training loss (scaled): 0.3718 [3/33]Training loss (scaled): 0.4041 [4/33]Training loss (scaled): 0.4045 [5/33]Training loss (scaled): 0.4658 [6/33]Training loss (scaled): 0.4331 [7/33]Training loss (scaled): 0.3931 [8/33]Training loss (scaled): 0.4214 [9/33]Training loss (scaled): 0.4358 [10/33]Training loss (scaled): 0.4421 [11/33]Training loss (scaled): 0.4126 [12/33]Training loss (scaled): 0.4233 [13/33]Training loss (scaled): 0.3572 [14/33]Training loss (scaled): 0.3760 [15/33]Training loss (scaled): 0.3989 [16/33]Training loss (scaled): 0.3936 [17/33]Training loss (scaled): 0.4368 [18/33]Training loss (scaled): 0.4128 [19/33]Training loss (scaled): 0.4697 [20/33]Training loss (scaled): 0.4104 [21/33]Training loss (scaled): 0.4207 [22/33]Training loss (scaled): 0.3813 [23/33]Training loss (scaled): 0.3743 [24/33]Training loss (scaled): 0.4106 [25/33]Training loss (scaled): 0.4231 [26/33]Training loss (scaled): 0.4358 [27/33]Training loss (scaled): 0.4773 [28/33]Training loss (scaled): 0.4075 [29/33]Training loss (scaled): 0.3992 [30/33]Training loss (scaled): 0.3733 [31/33]Training loss (scaled): 0.3323 [32/33]Epoch 12 endValidation loss at epoch 12 (scaled): 0.3552Validation loss at epoch 12: 0.7013Epoch 13 startTraining loss (scaled): 0.4077 [0/33]Training loss (scaled): 0.3345 [1/33]Training loss (scaled): 0.4136 [2/33]Training loss (scaled): 0.3936 [3/33]Training loss (scaled): 0.4302 [4/33]Training loss (scaled): 0.3457 [5/33]Training loss (scaled): 0.4199 [6/33]Training loss (scaled): 0.4307 [7/33]Training loss (scaled): 0.4023 [8/33]Training loss (scaled): 0.3308 [9/33]Training loss (scaled): 0.3813 [10/33]Training loss (scaled): 0.3892 [11/33]Training loss (scaled): 0.3499 [12/33]Training loss (scaled): 0.4666 [13/33]Training loss (scaled): 0.4937 [14/33]Training loss (scaled): 0.4275 [15/33]Training loss (scaled): 0.4087 [16/33]Training loss (scaled): 0.4822 [17/33]Training loss (scaled): 0.4170 [18/33]Training loss (scaled): 0.3948 [19/33]Training loss (scaled): 0.4583 [20/33]Training loss (scaled): 0.4229 [21/33]Training loss (scaled): 0.3940 [22/33]Training loss (scaled): 0.3770 [23/33]Training loss (scaled): 0.4866 [24/33]Training loss (scaled): 0.3835 [25/33]Training loss (scaled): 0.4238 [26/33]Training loss (scaled): 0.3699 [27/33]Training loss (scaled): 0.3833 [28/33]Training loss (scaled): 0.4583 [29/33]Training loss (scaled): 0.4092 [30/33]Training loss (scaled): 0.3901 [31/33]Training loss (scaled): 0.3960 [32/33]Epoch 13 endValidation loss at epoch 13 (scaled): 0.3552Validation loss at epoch 13: 0.7009Epoch 14 startTraining loss (scaled): 0.3989 [0/33]Training loss (scaled): 0.4541 [1/33]Training loss (scaled): 0.4031 [2/33]Training loss (scaled): 0.3794 [3/33]Training loss (scaled): 0.4490 [4/33]Training loss (scaled): 0.4451 [5/33]Training loss (scaled): 0.4978 [6/33]Training loss (scaled): 0.3982 [7/33]Training loss (scaled): 0.4253 [8/33]Training loss (scaled): 0.3896 [9/33]Training loss (scaled): 0.4092 [10/33]Training loss (scaled): 0.3547 [11/33]Training loss (scaled): 0.4739 [12/33]Training loss (scaled): 0.4065 [13/33]Training loss (scaled): 0.4004 [14/33]Training loss (scaled): 0.3972 [15/33]Training loss (scaled): 0.3875 [16/33]Training loss (scaled): 0.3767 [17/33]Training loss (scaled): 0.4216 [18/33]Training loss (scaled): 0.3386 [19/33]Training loss (scaled): 0.3823 [20/33]Training loss (scaled): 0.4116 [21/33]Training loss (scaled): 0.3882 [22/33]Training loss (scaled): 0.3708 [23/33]Training loss (scaled): 0.4268 [24/33]Training loss (scaled): 0.3677 [25/33]Training loss (scaled): 0.4009 [26/33]Training loss (scaled): 0.4165 [27/33]Training loss (scaled): 0.4329 [28/33]Training loss (scaled): 0.3398 [29/33]Training loss (scaled): 0.4089 [30/33]Training loss (scaled): 0.4509 [31/33]Training loss (scaled): 0.4446 [32/33]Epoch 14 endValidation loss at epoch 14 (scaled): 0.3620Validation loss at epoch 14: 0.6809((495,), (15,))
Plot the scaled training vs. validation loss. Our model performs remarkably well on both seen and unseen inputs!
import matplotlib.pyplot as pltbatch_total = training_losses_scaled.sizeepoch_total = validation_losses_scaled.sizebatches_per_epoch = batch_total // epoch_totalbatch_x = np.arange(batch_total)epoch_x = np.arange(epoch_total) * batches_per_epoch + batches_per_epochtraining_losses_y = training_losses_scaled.asnumpy()validation_losses_y = validation_losses_scaled.asnumpy()plt.figure(figsize=(8, 5))plt.plot(batch_x, training_losses_y, label='Training loss (scaled)', linestyle='-')plt.plot(epoch_x, validation_losses_y, label='Validation loss (scaled)', linestyle='--')plt.title('Training vs. validation loss (scaled)')plt.xlabel('Batch number')plt.ylabel('Loss (scaled)')plt.yscale('log')plt.grid(True, linestyle='--', alpha=0.6)plt.legend()plt.show()
.
Predicting the house price on a validation sample
Let’s take a sample from the validation set and use our model to predict the house price. We’ll see how it compares to the actual price and how much it differs.
Recall that:
- The features are normalized to have mean $\mu = 0$ and $\sigma = 1$ with scikit-learn’s
StandardScaler - The labels are transformed by the 2-step process below.
- Compute $\log (1 + y_i)$ for each label $y_i$
- Normalize the result in (a) with
StandardScaler
- The original labels are expressed as multiples of USD\$100,000
X_test_scaled_sample = X_test_scaled[0]y_test_scaled_sample = y_test_scaled[0].reshape(-1, 1)model.set_train(False)y_hat_scaled_sample = model(mindspore.Tensor(X_test_scaled_sample.astype(np.float16))).asnumpy().reshape(-1, 1)y_hat_sample = scaler.inverse_transform(y_hat_scaled_sample).item()y_hat_sample_usd = y_hat_sample * 100_000y_test_sample = scaler.inverse_transform(y_test_scaled_sample).item()y_test_sample_usd = y_test_sample * 100_000print(f'Predicted house price (USD$): {y_hat_sample_usd:>10.2f}')print(f'Actual house price (USD$): {y_test_sample_usd:>13.2f}')print(f'Percentage error: {(y_hat_sample_usd - y_test_sample_usd) / y_test_sample_usd * 100:>22.2f}%')
Predicted house price (USD$): 129003.91Actual house price (USD$): 165600.00Percentage error: -22.10%
Saving and exporting the model
Now that our linear regression model is trained to predict house prices in California, let’s save and export it so others can download and import our model for inference. The most common exported model formats supported by MindSpore include but not limited to the below.
- MindIR: the intermediate representation (IR) format natively supported by MindSpore. Use the
mindspore.exportfunction withfile_format='MINDIR'to export models in this format - ONNX: the leading portable, vendor-neutral format for representing predictive machine learning models, a graduated project under LF AI & Data. Use the
mindspore.exportfunction withfile_format='ONNX'to export models in this format
Let’s export our model in MindIR format and specify the following arguments.
net: our trained model*inputs: sample inputs that our model takes. Since each sample in our dataset has 8 features, our sample tensor has shape(1, 8)file_name: the name of our exported model, minus the file extensionfile_format: the format of our exported model. The appropriate file extension is automatically appended, e.g..mindir
# Export our model in MindIR format to `california-housing-linear-simple.mindir`mindspore.export(model, mindspore.Tensor(X_test_scaled_sample.astype(np.float16).reshape(-1, 8)), file_name='california-housing-linear-simple', file_format='MINDIR')# Verify the file existsos.path.isfile('california-housing-linear-simple.mindir')
True
To export our model in ONNX format, the file_format='ONNX' option is deprecated so we will use mindspore.onnx.export instead with the following parameters.
net: our trained model*inputs: sample inputs to our model, similar withmindspore.exportfile_name: filename of our exported ONNX model. The.onnxfile extension must be specified explicitlyinput_names: list of names for our model inputs, e.g.['features']output_names: list of names for our model outputs, e.g.['labels']
# Export our model in ONNX format to `california-housing-linear-simple.onnx`mindspore.onnx.export(model, mindspore.Tensor(X_test_scaled_sample.astype(np.float16).reshape(-1, 8)), file_name='california-housing-linear-simple.onnx', input_names=['features'], output_names=['labels'])# Verify the file existsos.path.isfile('california-housing-linear-simple.onnx')
True
With our model exported in both formats, we can upload them to object storage or a dedicated hub for sharing machine learning models such as Hugging Face. This is outside the scope of this article.
Concluding remarks and going further
We saw in this interactive notebook article how to train a simple linear regression model in MindSpore to predict house prices in California. The key points are summarized below.
- Loading the California housing dataset with scikit-learn
- Checking and preprocessing our data to ensure it is clean and well-structured
- Applying transformations to our data to ensure model accuracy and performance
- Defining the neural network, loss and optimizer functions for training our model
- Organizing our training set in batches of $2^n$ to manage the training workload and memory consumption
- Making predictions on our validation set and unwinding the data transformations to obtain meaningful figures
This experiment has only scratched the surface of what’s possible with MindSpore and the Ascend ecosystem. I hope you enjoyed this article and stay tuned for updates! 😉
Donald Sebastian Leung 
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